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|Grade 4 Mathematics Frameworks |

|Unit 1 |

|Whole Numbers, Place Value, and Rounding |

Unit 1

WHOLE NUMBERS, PLACE VALUE, AND ROUNDING

(6 weeks)

TABLE OF CONTENTS

Overview……………………………………………………………………………….…. 3

Key Standards & Related Standards……………………………………………………… 4

Enduring Understandings…………………………………………………………….…… 6

Essential Questions…………………………………………………………………...…… 6

Concepts & Skills to Maintain ……………………………………………………………. 7

Selected Terms and Symbols……………………………………………………………… 8

Classroom Routines ....………………………………………………………………….. 10

Strategies for Teaching and Learning ............................................................................... 10

Evidence of Learning………………………………………………………….…........….10

Tasks ……………………………………………………................................................. 11

• Number Scramble…………………………………………………………..….... 12

• Ticket Master…………………………………………………………….......…. 16

• Tri-Number Match………………………………………………………........… 21

• Traveling with Numbers...……………………………………………........…… 29

• Finding My Way Home …………………………………………….......……… 33

• Building Big Numbers………………………………………………........…….. 40

• Burger Delight……………………………………………………….........……. 45

• Newspaper Estimation………………………………………………........…….. 49

• Grocery Shopping………………………………………………………........…. 54

• Field Day Fun……………….…………………………………………........…... 58

Culminating Task

It’s in the Numbers! .....……………………………………………………………........ 62

OVERVIEW

In this unit students will:

• read numbers correctly through the millions

• write numbers correctly through millions in standard form

• write numbers correctly through millions in expanded form

• identify the place value name for hundredths through millions

• identify the place value locations for hundredths through millions

• round numbers to the nearest whole number, ten, hundred or thousand

• describe real life applications of applying rounding to the nearest ten, hundred and thousand

• order two-digit decimals

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as estimation, mental computation, and basic computation facts should be addressed on an ongoing basis.  Ideas related to the five process standards, problem solving, reasoning, connections, communication, and representation, should be addressed constantly as well. The first unit should establish these routines, allowing students to gradually enhance their understanding of the concept of number and to develop computational proficiency.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.

STANDARDS ADDRESSED IN THIS UNIT

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.

KEY STANDARDS

M4N1. Students will further develop their understanding of how whole numbers and decimals are represented in the base-ten numeration system.

a. Identify place value names and places from hundredths through one million.

b. Equate a number’s word name, its standard form, and its expanded form.

M4N2. Students will understand and apply the concept of rounding numbers.

a. Round numbers to the nearest ten, hundred, or thousand.

b. Describe situations in which rounding numbers would be appropriate and determine whether to round to the nearest ten, hundred, or thousand.

c. Determine to which whole number or tenth a given decimal is closest using tools such as a number line, and/or charts.

d. Round a decimal to the nearest whole number or tenth.

e. Represent the results of computation as a rounded number when appropriate and estimate a sum or difference by rounding numbers.

M4N5. Students will further develop their understanding of the meaning of decimals and use them in computations.

a. Understand decimals are a part of the base-ten system.

b. Understand the relative size of numbers and order two digit decimals.

c. Add and subtract both one and two digit decimals.

e. Multiply and divide both one and two digit decimals by whole numbers.

RELATED STANDARDS

M4N3. Students will solve problems involving multiplication of 2-3 digit numbers by 1-2 digit numbers.

M4N7. Students will explain and use properties of the four arithmetic operations to solve and check problems.

d. Use mental math and estimation strategies to compute.

M4A1. Students will represent and interpret mathematical relationships in quantitative expressions.

c. Write and evaluate mathematical expressions using symbols and different values.

M4P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving.

b. Solve problems that arise in mathematics and in other contexts.

c. Apply and adapt a variety of appropriate strategies to solve problems.

d. Monitor and reflect on the process of mathematical problem solving.

M4P2. Students will reason and evaluate mathematical arguments.

a. Recognize reasoning and proof as fundamental aspects of mathematics.

b. Make and investigate mathematical conjectures.

c. Develop and evaluate mathematical arguments and proofs.

d. Select and use various types of reasoning and methods of proof.

M4P3. Students will communicate mathematically.

a. Organize and consolidate their mathematical thinking through communication.

b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

c. Analyze and evaluate the mathematical thinking and strategies of others.

d. Use the language of mathematics to express mathematical ideas precisely.

M4P4. Students will make connections among mathematical ideas and to other disciplines.

a. Recognize and use connections among mathematical ideas.

b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

c. Recognize and apply mathematics in contexts outside of mathematics.

M4P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate mathematical ideas.

b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical phenomena.

ENDURING UNDERSTANDINGS

• The value of a number is determined by the place of its digits.

• Whole numbers are read from left to right using the name of the period.

• Numbers are written using commas to separate periods.

• Rounded numbers are approximate and not exact.

• Using rounding is an appropriate strategy for solving problems and estimating.

• A number can be written using its name, standard, or expanded form.

ESSENTIAL QUESTIONS

• How do digit values change as they are moved around in large numbers?

• What determines the value of a digit?

• How can we determine the sizes of numbers in comparison to each other?

• What determines the value of a number?

• How many different ways can a given number be written?

• How can we tell which forms of a number match each other?

• How do we round numbers to the nearest ten, hundred or thousand?

• Does rounding a number change its value relative to other numbers?

• What does it mean to round numbers to the nearest ten?

• In what situations might a person want to round a number to the nearest ten?

• How is rounding used in everyday life?

• How do you round a decimal?

• Why is it helpful to round decimal?

• In which situations should decimals be rounded?

• How does rounding a decimal make calculations easier?

• How does estimation keep us from having to count large numbers individually?

• How are large numbers estimated?

• How can multiplication be used to assist in the process of estimation?

• How can a grocery store advertising flyer help people spend their money wisely?

• How can we use the prices in a grocery store advertising flyer to decide how much money to take to the store with us?

• How can estimation help us shop?

• How can we tell how big a decimal number is?

• What do we need to know about numbers in order to put decimal numbers in order?

• What kinds of things are large numbers used to measure?

• What kinds of things are decimal numbers used to measure?

• How can we tell which number among many large numbers is the largest or smallest?

• How can we compare decimal numbers to each other?

• How do people use data to make decisions in their lives?

• How does numerical data inform us when choosing a place to live?

CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

• Fluency with reading numbers through 10,000

• Writing numbers through 10,000

• Comparing numbers in word form, number form, or expanded form

• Ordering large numbers

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and `how their students are able to explain and apply them.

The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

← Digits: The symbols used to make a number. In our number system (base ten), the digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In a place value system, the location of the digit determines it value. For example, in the number 427, the digit 4 is in the hundreds place, so its value is 400 (4 x 100). The digit 2 is in the tens place, so its value is 20 (2 x 10). The digit 7 is in the ones place, so its value is 7 (7 x 1).

← Equality/Inequality Symbols:

Equality

= Is equal to

Inequality

( Is not equal to

> Is greater than

< Is less than

← Estimate: An approximation of the actual value for the size, cost, or quantity of something; could be found through counting, computation, or rounding.

← Expanded Form: A way to write a number to show the place value of each digit Example: 34,088 is written as 30,000 + 4,000 + 80 + 8

← Numbers: Describe quantities or values

← Numerals: Symbols used to represent numbers (Hindu-Arabic – 0, 1, 2, ...; Roman I, II, III, ...; Word Name – twenty-one)

← Periods: Each group of three digits in a number

← Place Value: The value given to a digit based on its location in a number

← Rounding: Change a number to one that is approximate in value, but more convenient to use

The steps for rounding are given below.

o If the digit immediately following the specified place is 5 or more, add 1 to the digit in the specified place. This is rounding up.

Example: 8,287 rounded to the nearest hundred is 8,300 (8 is greater than 5)

o If the digit immediately following the specified place is less than 5, do not change the digit in the specified place. This is rounding down.

Example: 47,391 rounded to the nearest thousand is 47, 000 (3 is less than 5)

← Standard Form: A way to write a number to show only each digit

Example: 1,491is in standard form, in expanded form it would be written as 1,000 + 400 + 90 + 1

CLASSROOM ROUTINES

The importance of establishing classroom routines cannot be overstated. Daily routines must include such obvious activities as estimating, analyzing data, describing patterns, and answering daily questions. They should also include less obvious routines, such as how to select materials, how to use materials in a productive manner, how to put materials away, and how to access classroom technology such as computers and calculators. An additional routine is to allow plenty of time for children to explore new materials before attempting any directed activity with these new materials.  The regular use of routines is important to the development of students' number sense, flexibility, fluency, collaborative skills, and communication. These routines contribute to a rich, hands-on standards based classroom and will support students’ performances on the tasks in this unit and throughout the school year.

STRATEGIES FOR TEACHING AND LEARNING

• Students should be actively engaged by developing their own understanding.

• Mathematics should be represented in as many ways as possible by using graphs, tables, pictures, symbols, and words.

• Appropriate manipulatives and technology should be used to enhance student learning.

• Students should be given opportunities to revise their work based on teacher feedback, peer feedback, and metacognition which includes self-assessment and reflection.

• Students should write about the mathematical ideas and concepts they are learning.

EVIDENCE OF LEARNING

By the conclusion of this unit, students should be able to demonstrate the following competencies:

• read numbers to one million and to hundredths

• write numbers in the millions using commas to indicate periods and in the hundredths using the decimal point correctly

• recognize numbers in standard, expanded, and word form

• round numbers to the nearest 0.1s, 1s, 10s, 100s, and 1000s

• compare rounded numbers and express their relationship using >, ................
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